RFE October 2026: Coefficients of Legendre polynomials

[Sean A. Irvine]

Hi,

With the preparations for A400K, I've had less time than usual to find a good topic for the month, so here is what I hope will be a simple one:

The following 12 sequences all have the same name: Coefficients of Legendre polynomials: A001795, A001796, A001797, A001798, A001799, A001800, A001801, A001802, A002461, A002462, A002463, A006750.

Can someone please take a look and propose distinct names?

Some progress was made on last month's request, but it's not quite ticked off.

I track these requests for enhancement here (a few others still remain open):

https://oeis.org/wiki/User:Sean_A._Irvine/Requests_for_Enhancements#Requests_for_Enhancements

Sean.

[Ed Pegg]

A001795 — Coefficient of P_0(x) in the Legendre expansion of x^n
A001796 — Coefficient of P_1(x) in the Legendre expansion of x^n
A001797 — Coefficient of P_2(x) in the Legendre expansion of x^n
A001798 — Coefficient of P_3(x) in the Legendre expansion of x^n
A001799 — Coefficient of P_4(x) in the Legendre expansion of x^n
A006750 — Coefficient of P_5(x) in the Legendre expansion of x^n 

x^0 = P_0(x)
x^1 = P_1(x)
x^2 = (P_0(x) + 2 P_2(x))/3
x^3 = (3 P_1(x) + 2 P_3(x))/5
x^4 = (7 P_0(x) + 20 P_2(x) + 8 P_4(x))/35
x^5 = (27 P_1(x) + 28 P_3(x) + 8 P_5(x))/63
x^6 = (33 P_0(x) + 110 P_2(x) + 72 P_4(x) + 16 P_6(x))/231
x^7 = (143 P_1(x) + 182 P_3(x) + 88 P_5(x) + 16 P_7(x))/429

Reading down the columns gives

P_0: 1, 1, 7, 33, ... = A001795
P_1: 1, 3, 27, 143, ... = A001796
P_2: 2, 20, 110, ... = A001797
P_3: 2, 28, 182, ... = A001798
P_4: 8, 72, ... = A001799
P_5: 8, 88, ... = A006750

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[Sean A. Irvine]

Thanks Ed, I have applied those names.

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAGog0%2BY0RtPw%3DSZL1fDfqL%3DvMnfH2xUU279C6sbwpbgHsbrxWg%40mail.gmail.com.

[Ed Pegg]

Maybe this graphic would help?  

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAL0FET%3Dtmj5wQxC%2BTUKeht_-JJQ8HB51_nbawveTEuBe90L_XQ%40mail.gmail.com.

[Ed Pegg]

Disregard the graphic... there are errors.