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A329756 Doubly heptagonal pyramidal numbers. 4
0, 1, 456, 14976, 181780, 1273970, 6293756, 24395756, 79119496, 223821235, 568280240, 1321714636, 2858876956, 5817509516, 11237224740, 20751835560, 36849296016, 63215722181, 105182448536, 170297734920, 269047574180, 415753060646, 629674964556, 936359517556 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..23.

Eric Weisstein's World of Mathematics, Heptagonal Pyramidal Number

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

G.f.: x*(1 + 446*x + 10461*x^2 + 52420*x^3 + 75580*x^4 + 32544*x^5 + 3504*x^6 + 44*x^7)/(1 - x)^10.

a(n) = A002413(A002413(n)).

a(n) = Sum_{k=0..A002413(n)} A000566(k).

a(n) = n *(5*n-2) *(n+1) *(5*n^3+3*n^2-2*n+6) *(25*n^3+15*n^2-10*n-12)/1296. - R. J. Mathar, Nov 28 2019

MATHEMATICA

A002413[n_] := n (n + 1) (5 n - 2)/6; a[n_] := A002413[A002413[n]]; Table[a[n], {n, 0, 25}]

Table[Sum[k (5 k - 3)/2, {k, 0, n (n + 1) (5 n - 2)/6}], {n, 0, 25}]

nmax = 25; CoefficientList[Series[x (1 + 446 x + 10461 x^2 + 52420 x^3 + 75580 x^4 + 32544 x^5 + 3504 x^6 + 44 x^7)/(1 - x)^10, {x, 0, nmax}], x]

LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 456, 14976, 181780, 1273970, 6293756, 24395756, 79119496, 223821235}, 26]

CROSSREFS

Cf. A000566, A002413, A140236, A264891, A329753, A329754, A329755, A329757.

Sequence in context: A222552 A200784 A077578 * A268162 A223750 A048110

Adjacent sequences:  A329753 A329754 A329755 * A329757 A329758 A329759

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Nov 20 2019

STATUS

approved

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Last modified May 28 03:04 EDT 2020. Contains 334671 sequences. (Running on oeis4.)